Download Economics 304 Fall 2014 Country-Analysis Project Part 4: Economic

Economics 304
Country-Analysis Project
Fall 2014
Part 4: Economic Growth Analysis
Introduction
In this part of the project, you will analyze the economic growth performance of your
country over the available sample period. The sections below describe a set of analyses that
can be performed. Your report should roughly (or exactly) include sections corresponding to
the sections of the assignment.
For this part of the project, you should download the appropriate series from the Penn
World Tables (http://www.rug.nl/research/ggdc/data/penn-world-table), which is the
leading data source for internationally comparable GDP series. The PWT series are limited
to annual data, but they are measured in PPP-equivalent real U.S. dollars, which makes
them highly suitable for long-run analysis. The data are available for most countries since
1950 or 1960 and have been adjusted to the extent possible to account for changes in
measurement over time.
To access the data you need, select the “GA” (growth accounting) link from the list of
queries. Once this opens up, click “Adjust criteria” at the top. Under the Variables tab, add
in population and share of labor compensation to the ones already selected. Under the
“Regions” tab, deselect the countries that are selected and choose the one(s) you want. Then
click the Results link at the top to see the table. If it’s not quite right, toggle back to adjust
criteria and try again. Once you get the series you want, click on “Export to .XLSX” above
the data table. The data series will be on the second tab of the downloaded Excel spreadsheet
and should look something like the figure below. (Note that my demonstrations here are
from Excel for Windows. The Mac version may looks somewhat different.)
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When you download the data, you will probably find a small green triangle in the top left
corner of the data cells. This indicates that there is an issue with the formatting of the cell, in
this case that the cell is formatted as text rather than as a number. You will need to change
this. To do so, select all of the affected data cells (most likely those in columns C and D
starting in row 2). When you select one or more of these cells, an icon with an exclamation
mark inside a yellow diamond should appear next to the cells. Click this icon to open a
menu of choices as shown below.
Click on “Convert to Number” and the cells should become numeric, with the green triangle
disappearing. You are now ready to create your dataset.
If will be easier to work with the data if you create a new spreadsheet with the variables in
columns next to each other. You can copy and paste the numbers from the downloaded
spreadsheet into the new spreadsheet one variable at a time. Put the variable names in the
top row just to keep things straight. Your dataset should then look something like this, with
no green triangles or exclamation marks:
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I recommend that you conduct the various steps of your analysis in separate spreadsheets
(tabs) within a single Excel workbook. Name the first tab (which you have just created) Data
by double-clicking on the tab (where it says Sheet1) at the bottom of the screen and typing
the new name. Before starting to analyze your data, make one last check to make sure
everything looks right.
Informal assessment of real GDP growth
Begin your analysis with an informal examination of the behavior of real GDP and percapita GDP during your sample. To do this, copy the column for year, population (pop), and
real GDP (rgdpna) to a new sheet/tab. Create a new variable for per-capita real GDP by
dividing GDP by population: type =C2/B2 into cell D2, then copy cell D2 and paste it into
the cells below it in column D all the way to the bottom of the table. Your sheet should look
something like this:
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When analyzing economic growth, we use the (natural) logarithm of the variable rather than
its level. A variable growing at a constant percentage rate will follow an upward-curving
exponential path such as the one below:
The mathematical formula for this curve is y ( t ) = y ( 0 ) e gt with g being the constant rate of
growth and y(0) the level of y when t = 0. Our eyes are not used to assessing exponential
functions, so would be difficult to distinguish the constant-growth-rate diagram above from
one that curved up a bit more (an increasing growth rate) or a bit less (a decreasing growth
rate).
If we take the log of this equationn, we get log
=
( y ( t ) ) log ( y ( 0 ) ) + log ( e gt ) , or
log ( y ( t ) )= a + gt , with a = log(y(0)) and g being the growth rate. This is a linear function of
time whose slope is equal to the growth rate g, so if we plot the log of GDP it will be a
straight line if the GDP is growing at a constant rate, as shown below
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If the series curves upward (downward), then the slope and growth rate are increasing
(decreasing). Our eyes are good at detecting deviations from straight lines, so graphing
growing time series in log form makes it easy to see how the growth rate varies over time.
Construct a time plot of (1) the log of real GDP and (2) the log of per-capita real GDP for
your country using the graph features of Excel (on the Insert menu). Based on your graphs,
• Does the growth rate of each variable appear roughly constant over time or are there
breakpoints at which the growth rate increases or decreases?
• Are there periods of recession or boom when the economy seems to be well below or
above its steady-state path?
Put the graph and your analysis into your report for this week’s project, which will become a
chapter of your full analysis.
Estimating a growth trend
Your time plots of log real GDP and log real per-capita GDP are unlikely to be exactly
straight lines. We can estimate the growth relationship over the sample period by running a
linear regression of log GDP on time—essentially we are estimating the coefficients a and g in
the equation log ( y ( t ) )= a + gt to give the “best fit” over the sample, minimizing the
squared vertical deviations from the fitted line.
Regressions are very easily done in Stata, but for this exercise we can use Excel equally
easily. To estimate the slope (g) of the relationship between log GDP (either one) and year,
click on an empty cell and use the SLOPE function. For example, if the log real GDP series
is in cells E2:E63 and the years are in B2:B63, then type
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=100*slope(E2:E63,B2:B63)
to calculate the slope of the best-fit line and multiply it by 100 to put the result in percentage
terms. (It will help you keep things straight if you use the cell above the calculation to type in
a label telling what the number is.)
Using the full sample, what are the trend growth rates of real GDP and per-capita real GDP
for your country? If there seemed from your visual inspection that there were breakpoints
where the slope of the trend line changed, perform separate trend regressions for the subsamples before and after the break. (Include the year of the break in both sub-samples.) Does
there seem to be a large difference in the estimated trend growth rates before and after the
break? (There are ways to test this statistically, but you would need Stata to do this so it is
not required. Those of you who have taken Econ 311 or 312 are encouraged to do this.
Come and talk to me to get more instructions.)
Average vs. trend growth rates
The average growth rate over the period T1 to T2 can be calculated as
=
g 100 ×
log ( y (T2 ) ) − log ( y (T1 ) )
T2 − T1
.
Calculate the average growth rates over the full available sample and compare it to the trend
rate? Are they larger or smaller? Why?
Average growth rates are very sensitive to the choice of endpoints T1 and T2. Starting the
period in the middle of a recession and ending it during a boom yields a higher average
growth rate. Similarly, starting in a boom and ending in a recession gives a smaller average
growth rate. If you were trying to make an optimistic case for growth in your country, what
starting and ending years (within a few years of the beginning and end of the sample,
respectively) would you choose? What if you were trying to be pessimistic? How much
difference does it make?
Convergence
One of the key implications of the Solow growth model is that countries with similar
parameters (saving rate, population growth rate, production function, etc.) but different
initial capital/labor ratios should eventually converge to similar levels of per-capita GDP.
This implies that countries (again, with similar parameters) that start further below the leader
country should grow faster than the leader.
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Assess the degree of convergence for your country by calculating its initial per-capita GDP
gap relative to the U.S. (early-period U.S. numbers are in the Excel demonstration tables
above, or can be obtained from the PWT online) and comparing its per-capita growth rate to
the U.S. rate (0.92% from 1950 to 2011). Empirical evidence suggests that each 1% gap in
initial GDP results in a growth rate that is about 0.02% points higher, so a country that starts
20% below the U.S. should grow about 0.4% points per year more quickly than the U.S. (i.e.,
at about 1.32% per year). How does your country measure up to the statistical average? Has
it growth faster or slower than predicted by the empirical evidence, given its initial gap?
In the paper on the reading list by Xavier Sala-i-Martin, he finds that there are a couple of
dozen variables that help explain why some countries grow faster and others more slowly
than the simple convergence hypothesis would predict. Look at these variables. Based on
what you know about your country, which (if any) of these variables seems like it would
have an important effect in raising or lowering growth relative to the average convergence
path?
Basic growth accounting and Solow residuals
One of the earliest and most fundamental modes of growth analysis is attempting to break
down the growth of GDP into components due to increases in the capital stock, increases in
labor input, and improvements in total factor productivity—so-called “growth accounting.”
The “GA” dataset within the Penn World Tables was designed to facilitate growth
accounting by providing time series for real GDP, employment, human capital per worker,
and capital input.
From the data you have downloaded, you can calculate the growth rates of employment,
human capital per worker, and capital input. In order to combine the labor and capital inputs
we need to know how much each contributes at the margin to output. Suppose that we
approximate the aggregate production function for your economy as
Yt = At K tα ( H t Lt )
1−α
,
where A is an index of total factor productivity (TFP), K is capital input, H is human capital
per worker, and L is employment. Taking logs gives
log
=
(Yt ) log ( At ) + α log ( K t ) + (1 − α ) ( log ( H t ) + log ( Lt ) ) ,
or
yt= at + αkt + (1 − α )( ht + l t )
where lower-case letters represent the logs of the corresponding capital-letter variables.
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The growth rate of any variable X from period t − 1 to period t can be written as
log ( X t ) − log ( X t −1 ) , so by differencing the log equation we get an equation for growth rates:
( yt − yt −1=) ( at − at −1 ) + α ( kt − kt −1 ) + (1 − α )( ht − ht −1 ) + (1 − α )( lt − lt −1 ).
Using your data, you can calculate year-to-year growth rates for GDP, capital, human
capital per worker, and employment, but we have no independent information on TFP. The
task of growth accounting is to break down total GDP growth into the four components
shown in the last equation: those due to physical capital, human capital, employment
growth, and growth in TFP. We calculate the latter by solving for
( at − at −1=) ( yt − yt −1 ) − α ( kt − kt −1 ) − (1 − α )( ht − ht −1 ) − (1 − α )( lt − lt −1 ).
All we need (besides the data) is an estimate of the α parameter, which is the elasticity of
output with respect to capital. This is approximately equal to “capital’s share” of GDP,
which can be measured. The PWT data provide a variable labsh, which is an estimate of
labor’s share, or 1 − α. The only problem is that their measure of 1 − α is not constant but
varies from year to year. So when calculating growth from year t − 1 to t, should we use that
value of α for year t, the value for year t − 1, or the average of the two? The last option is
probably the best, so our formula for TFP growth in period t becomes
( at − at −1 ) = ( yt − yt −1 ) −
α t + α t −1
α +α
α +α
( kt − kt −1 ) −  1 − t t −1  ( ht − ht −1 ) −  1 − t t −1  ( lt − lt −1 ).
2
2
2




To perform your growth accounting exercise for your country, you should construct
formulas in your Excel spreadsheet to create a table with adjacent columns measuring GDP
 α + α t −1
growth ( yt − yt −1 ) , the contribution of capital growth to GDP growth  t
( kt − kt −1 )  ,
2


  α + α t −1 

the contribution of human-capital growth to GDP growth   1 − t
( ht − ht −1 )  , the

2



  α + α t −1 

contribution of employment growth to GDP growth   1 − t
( lt − lt −1 )  , and TFP

2



growth ( at − at −1 ) , calculated according to the formula above. Using your table, which
components have contributed the most on average to GDP growth in your country? Have
the contributions varied over time? Assess your evidence.
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Once you have done this, calculate a series for the growth rates of the rtfna variable in the
PWT data (which is their measure of TFP). Does your measure match? (It should.)
Conclusion
Now that you have analyzed the growth experience of your country in detail, summarize
your conclusions. What are the important characteristics of growth in this country over your
sample? What, if anything, seems different from the “standard” case that we described in
class?
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